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Binomial Coefficient Calculator — result sheet
Calculate the exact number of ways to choose k items from n items without regard to order.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: C(n,k)=n!/(k!(n−k)!).
Symmetry is used by selecting the smaller of k and n−k before exact integer multiplication.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Total items n — minimum 0; maximum 500
- Selected items k — minimum 0; maximum 500
Worked example
| Input | Value |
|---|---|
| Total items n | 10 |
| Selected items k | 3 |
Binomial coefficient = 120.
Assumptions and limits
- n and k are whole numbers with 0≤k≤n.
- Items are distinct and order does not matter.
- Sampling replacement, probability, and dependent selection rules are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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